ASReml-S reference manual - VSN International

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8.6 Spatial analysis of a field experiment 98The iterative sequence has converged to column and row correlation parameters of0.68378 and 0.45851, respectively. The plot size and orientation is not known and soit is not possible to ascertain whether these values are spatially sensible. It is generallyfound that the closer the plot centroids, the higher the spatial correlation. This is notalways the case and if the highest between plot correlation relates to the larger spatialdistance then this may suggest the presence of extraneous variation [Gilmour et al., 1997,for example]. The plot of the sample variogram of the residuals is not trimmed and, ignoringthe unreliable contribution from extreme lags, appears in reasonable agreementwith the model.An extension to this model includes a measurement error or nugget effect term:> barley2.asr summary(barley2.asr)$loglik[1] -696.8227> summary(barley2.asr)$varcompgamma component std.error z.ratio constraintunits 0.1061724 4.859930e+03 1.787849e+03 2.718311 PositiveR!variance 1.0000000 4.577396e+04 1.667323e+04 2.745357 PositiveR!Row.ar1 0.6826403 6.826403e-01 1.022940e-01 6.673317 UnconstrainedR!Column.ar1 0.8437888 8.437888e-01 6.848144e-02 12.321425 Unconstrained> wald(barley2.asr)Wald tests for fixed effectsResponse: yieldTerms added sequentially; adjusted for those aboveDf Sum of Sq Wald statistic Pr(Chisq)(Intercept) 1 11918530 260 < 2.2e-16 ***Variety 24 11237959 246 < 2.2e-16 ***residual (MS) 45774The lattice analysis (with recovery of inter-block information) is:> barley3.asr summary(barley3.asr)$$loglik[1] -707.7857> summary(barley3.asr)$$varcompgamma component std.error z.ratio constraintRep 0.5287136 4262.361 6886.823 0.6189155 PositiveRowBlk 1.9344361 15594.957 5090.787 3.0633685 PositiveColBlk 1.8372487 14811.456 4865.667 3.0440754 PositiveR!variance 1.0000000 8061.759 1340.449 6.0142228 Positive
8.6 Spatial analysis of a field experiment 99> wald(barley3.asr)Wald tests for fixed effectsResponse: yieldTerms added sequentially; adjusted for those aboveDf Sum of Sq Wald statistic Pr(Chisq)(Intercept) 1 9808702 1217 < 2.2e-16 ***Variety 24 1711179 212 < 2.2e-16 ***residual (MS) 8062This variance model is not competitive with the preceding spatial models. The modelscan be formally compared using the BIC values, for example.The Wald statistics for the spatial models are greater than that for the lattice analysis(Table 8.7). We note that the Wald statistic for the spatial model including the nuggeteffect is smaller than that for the AR1×AR1 model.modelTable 8.7. Summary of models fitted to the Slate Hall dataREML log-likelihood parameters Wald statistic sedAR1×AR1 -700.32 3 312.82 59.0AR1×AR1 + units -696.82 4 245.49 60.5incomplete block -707.79 4 212.26 62.0Finally, we predict Variety means for each model using the predict() method. Only thefirst five and final three means are reproduced here. The overall SED is the square rootof the average variance of difference between the variety means. The two spatial analyseshave a range of SEDs which may be obtained in matrix form from the sed argument ofpredict(). Note that all variety comparisons have the same SED for the balanced latticesquare analysis.> barley1.pv barley1.pv$predictions$Variety$pvalsVariety predicted.value standard.error estStatus1 1 1257.981 64.61878 Estimable2 2 1501.442 64.98267 Estimable3 3 1404.987 64.63038 Estimable4 4 1412.569 64.90703 Estimable5 5 1514.480 65.59318 Estimable...23 23 1311.490 64.07718 Estimable24 24 1586.785 64.70481 Estimable25 25 1592.021 63.59445 Estimable> barley1.pv$predictions$Variety$avsed[1] 59.05192> barley2.pv barley2.pv$predictions$Variety$pvals
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Analysis of mixed modelsfor S langu
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D.G. ButlerQueensland Department of
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ContentsPreface . . . . . . . . . .
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ContentsviiB Available variance mod
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List of Figures1.1 Weekly body weig
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1.3 Data sets used 21.2.2 Help and
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1.3 Data sets used 41.3.2 Repeated
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1.3 Data sets used 6101 Sire 1 0102
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2.1 The linear mixed model 8Direct
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2.2 Estimation 10There is a corresp
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2.2 Estimation 12where H ij = ∂ 2
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2.5 Inference for random effects 14
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2.6 Inference for fixed effects 16T
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2.6 Inference for fixed effects 18t
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3Fitting the mixed model3.1 Introdu
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3.3 Introducing the asreml function
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3.6 Getting help3.7 The asreml func
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3.8 Fixed terms 26na.method.Xkeep.o
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3.8 Fixed terms 28Summary of reserv
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3.10 Conditional factors: the at()
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Table 3.2. Families and link functi
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3.15 Multivariate analysis 34R!trai
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Source df F_inc F_con MSource df dd
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4.1.1 Specifying variance models in
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4.2 A sequence of structures for th
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Σ = [σ ij ] :{σii = σ 2 , ∀i
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4.4 Variance model functions 44init
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The Matérn class4.4 Variance model
Page 60 and 61: 4.4 Variance model functions 48Chol
Page 62 and 63: Required argumentsobj4.5 Rules for
Page 64 and 65: 4.7 Constraining variance parameter
Page 66 and 67: 5Genetic analysis5.1 IntroductionIn
Page 68 and 69: 5.2 Pedigree, G-inverse objects and
Page 70 and 71: 5.4 Using Pedigree and G-inverse ob
Page 72 and 73: 6Prediction from the linear model6.
Page 74 and 75: Optional argumentslevels6.2 The pre
Page 76 and 77: 6.2 The predict method 64The predic
Page 78 and 79: 6.4 Complicated weighting 666.4 Com
Page 80 and 81: 7The asreml class and related metho
Page 82 and 83: maxiter maximum number of iteration
Page 84 and 85: 7.3 Methods and related functions 7
Page 88 and 89: pedigree7.3 Methods and related fun
Page 92 and 93: 8Examples8.1 IntroductionThis secti
Page 94 and 95: 8.2 Split Plot Design 82In this exa
Page 96 and 97: 8.3 Unbalanced nested design 84[4,]
Page 98 and 99: 8.3 Unbalanced nested design 86adju
Page 100 and 101: 8.4 Sources of variability in unbal
Page 102 and 103: 8.5 Balanced repeated measures 902
Page 104 and 105: 8.5 Balanced repeated measures 92Ta
Page 106 and 107: 8.5 Balanced repeated measures 94wh
Page 108 and 109: 8.6 Spatial analysis of a field exp
Page 112 and 113: Variety predicted.value standard.er
Page 114 and 115: 8.7 Unreplicated early generation v
Page 116 and 117: 8.7 Unreplicated early generation v
Page 118 and 119: 8.8 Paired Case-Control Study 106Th
Page 120 and 121: Terms added sequentially; adjusted
Page 122 and 123: 8.8 Paired Case-Control Study 110[
Page 124 and 125: 8.8 Paired Case-Control Study 112..
Page 126 and 127: 8.9 Balanced longitudinal data - Ra
Page 134 and 135: A.3 Aliasing and singularities 122W
Page 136 and 137: Table B.1: Details of the available
Page 138 and 139: B Available variance models 126Deta
Page 140 and 141: ReferencesG. E. P. Box. Analysis of
Page 142 and 143: References 130W. W. Stroup, P. S. B
Page 144 and 145: Index 132F statistics, 17fa(,k), 49
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